2.4 Relationship of Risk and Return

Valuing financial assets under
conditions of certainty is a breeze. The challenge is
to value assets in the real world of uncertainty -- of
risk. If we can relate risk and returns, such as by discounting
returns depending on their risk, we can value them!

How does one value a distribution of possible returns?
One method would be to estimate the relative probability
of different future possibilities and then discount
them to present value. For example, if we believed it
was equally likely that an investment after one year
would produce either $5 or $12 or $20, and the current
rate for a risk-free one-year investment were 6.3%,
we could compute the investment's present value as follows.
(More 2.4.1>>)

Another method to value a range of future results is
to find the present value of their "certainty equivalents."
Return to our example of an investment that will return
either $5 or $12 or $20 after one year, with an assumed
current rate of 6.3% for a risk-free one-year investment.
Perhaps we could determine the expected value of this
investment, and then determine the equivalent certain
amount this investment is worth, given the variability
of its returns. Once we determine this "certainty
equivalent" we could then compute its present value
-- thus. the investment's value. (More
2.4.2>>)

Another method for valuing future returns is to focus
on the volatility of the expected return and adjust
the discount rate to account for this volatility.
(In this way the discount rate compensates for two financial
elements -- volatility risk and time
value of money.) (More 2.4.3>>)